Geometry

Quadrilaterals

Quadrilateral Classification

         

Figure ABCDABCD is a parallelogram with AB=7\lvert{\overline{AB}} \rvert =7 and AD=10.\lvert{\overline{AD}}\rvert=10. If the points E,F,GE,F,G and HH are intersections between the angular bisectors of the four internal angles of the the parallelogram, what type of quadrilateral is EFGH EFGH?

Note: The above diagram is not drawn to scale.

ABCDABCD is a parallelogram and point MM is the midpoint of side AD\overline{AD} where AB=10,AD=12.\lvert{\overline{AB}}\rvert=10, \lvert{\overline{AD}}\rvert=12. If BM=CM,\lvert{\overline{BM}}\rvert=\lvert{\overline{CM}}\rvert, what type of quadrilateral is ABCDABCD?

Note: The above diagram is not drawn to scale.

In the above diagram, figure ABCDABCD is a parallelogram where AB=6\lvert{\overline{AB}} \rvert =6 and AD=8.\lvert{\overline{AD}}\rvert=8. If the angle bisectors of A\angle A and B\angle B intersect with BC\overline{BC} and AD\overline{AD} at EE and F,F, respectively, which of the following must be true of quadrilateral ABEF?ABEF ?

In the above diagram, points EE and FF are the feet of perpendiculars drawn from vertex AA of parallelogram ABCDABCD to sides BC\overline{BC} and CD,\overline{CD}, respectively. If AE=AF=13,\lvert{\overline{AE}}\rvert=\lvert{\overline{AF}}\rvert=13, what type of quadrilateral is ABCDABCD?

Note: The above diagram is not drawn to scale.

Figure ABCDABCD is a square with side length 1212 and EB=FC=GD=HA=9.\lvert{\overline{EB}}\rvert =\lvert{\overline{FC}}\rvert=\lvert{\overline{GD}}\rvert=\lvert{\overline{HA}}\rvert=9. What type of quadrilateral is EFGHEFGH?

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